Mathematics

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Graduate Courses

The faculty has approval to offer the following courses in the academic years 2003-2004 and 2004-2005; however, not all courses are taught each semester or summer session. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.

Unless otherwise stated below, each course meets for three lecture hours a week for one semester.

Mathematics: M

380C. Algebra.
A survey of algebraic structures, including groups, fields, rings, and modules. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.

381C. Real Analysis.
Same as Computational and Applied Mathematics 381R. Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.

381D. Complex Analysis.
Same as Computational and Applied Mathematics 381D. Introduction to complex analysis. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.

381E. Functional Analysis.
Same as Computational and Applied Mathematics 381S. Introduction to functional analysis. Prerequisite: Graduate standing, consent of instructor or the graduate adviser, and Computational and Applied Mathematics 381R or Mathematics 381C.

384G. Regression Analysis.
Fitting linear models to data by the method of least squares, choosing best subsets of predictors, and related materials. Prerequisite: Graduate standing and consent of instructor.

384H. Multivariate Statistical Analysis.
Introduction to the general multivariate linear model; a selection of techniques, such as principle component, factor, and discriminant analysis. Prerequisite: Graduate standing and consent of instructor.

385C. Theory of Probability.
Same as Computational and Applied Mathematics 384K. Prerequisite: Graduate standing and consent of instructor.

385D. Theory of Probability.
Same as Computational and Applied Mathematics 384L. Continuation of Mathematics 385C. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 384K or Mathematics 385C.

389J. Probability Models with Actuarial Applications.
Probability models with actuarial applications, including Markov chains, Brownian motion, the Black-Scholes formula, frequency-of-loss and severity-of-loss random variables, compound distributions, and ruin theory. With Mathematics 389U and 389V, covers the syllabus for exam #3 of the Society of Actuaries and the Casualty Actuarial Society. Four lecture hours a week for one semester. Prerequisite: Graduate standing, Mathematics 341 or 340L, and Mathematics 362K.

389T. Time Series and Survival-Model Estimation.
Introduction to the probabilistic and statistical properties of time series; parameter estimation and hypothesis testing for survival models. Covers 30 percent of the syllabus for exam #4 of the Society of Actuaries and the Casualty Actuarial Society. Prerequisite: Graduate standing, Mathematics 358K or 378K, and Mathematics 389U.

389V. Actuarial Contingent Payments II.
Mathematical analysis of insurance premiums, reserves, multiple-status survival models, multiple-decrement survival models; applications to such areas as life insurance and property/casualty insurance. With Mathematics 389J and 389U, covers the syllabus for exam #3 of the Society of Actuaries and the Casualty Actuarial Society. Four lecture hours a week for one semester. Prerequisite: Graduate standing, and Mathematics 389U or 339U.

390C. Topics in Algebra.
Recent topics have included algebraic geometry, number theory, algebraic curves, algebraic number theory, algebraic functions, rational curves on varieties, homological algebra. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

391C. Topics in Analysis.
Same as Computational and Applied Mathematics 391C. Recent topics have included measure and integration, real variables, complex analysis, functional analysis, ordinary differential equations, partial differential equations, integral transforms, operator theory, approximation theory, abstract harmonic analysis. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

392C. Topics in Topology.
Recent topics have included algebraic topology, differential topology, geometric topology, Lie groups. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

393D. Topics in Numerical Analysis.
Same as Computational and Applied Mathematics 393D. Recent topics have included numerical methods in ordinary differential equations, numerical methods in partial differential equations, computational problems in linear algebra, numerical solution of systems of equations, numerical methods in functional approximation, numerical integration. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

394C. Topics in Probability and Statistics.
Same as Computational and Applied Mathematics 394C. Recent topics have included nonparametric statistics, advanced probability. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

395C. Topics in Logic and Foundations.
Recent topics have included set theory, model theory, proof theory, axiomatic theorem proving, automatic theorem proving, foundations of mathematics, recursion theory. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

396C. Topics in Mathematics.
Recent topics have included set theory, history of mathematics. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

197S, 397S. Seminar in Mathematics.
One or three lecture hours a week for one semester. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule.Prerequisite: Graduate standing and consent of instructor.

698. Thesis.
The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in mathematics and consent of the graduate adviser; for 698B, Mathematics 698A.

398R. Master's Report.
Preparation of a report to fulfill the requirement for the master's degree under the report option. The equivalent of three lecture hours a week for one semester. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in mathematics and consent of the supervising professor and the graduate adviser.